Solve 1/z-1/p=1/q

$$\frac{ 1 }{ z } - \frac{ 1 }{ p } = \frac{ 1 }{ q }$$

Solve for p

$$p=\frac{qz}{q-z}$$

$$z\neq 0\text{ and }q\neq 0\text{ and }z\neq q$$

Steps for Solving Linear Equation

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by pqz, the least common multiple of z,p,q.

$$pq-qz=pz$$

Subtract pz from both sides.

$$pq-qz-pz=0$$

Add qz to both sides. Anything plus zero gives itself.

$$pq-pz=qz$$

Combine all terms containing p.

$$\left(q-z\right)p=qz$$

Divide both sides by -z+q.

$$\frac{\left(q-z\right)p}{q-z}=\frac{qz}{q-z}$$

Dividing by -z+q undoes the multiplication by -z+q.

$$p=\frac{qz}{q-z}$$

Variable p cannot be equal to 0.

$$p=\frac{qz}{q-z}\text{, }p\neq 0$$

Solve for q

$$q=\frac{pz}{p-z}$$

$$z\neq 0\text{ and }p\neq 0\text{ and }z\neq p$$

Steps for Solving Linear Equation

Variable q cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by pqz, the least common multiple of z,p,q.

$$pq-qz=pz$$

Reorder the terms.

$$-qz+pq=pz$$

Combine all terms containing q.

$$\left(-z+p\right)q=pz$$

The equation is in standard form.

$$\left(p-z\right)q=pz$$

Divide both sides by p-z.

$$\frac{\left(p-z\right)q}{p-z}=\frac{pz}{p-z}$$

Dividing by p-z undoes the multiplication by p-z.

$$q=\frac{pz}{p-z}$$

Variable q cannot be equal to 0.

$$q=\frac{pz}{p-z}\text{, }q\neq 0$$